Shared Network install / config priority
Blender searches three places for a startup file in the following order -


local  - located next to the blender application.
user   - located in the users home folder.
system - located in a shared system location (like /usr/share)


When you save your settings it is saved to the same location as it would be read from at startup.

This works well with the way blender allows you to have multiple copies on your machine, each can have their own config settings unique to that copy.

In your situation you have the local settings in a shared location that you consider a system location.

One option is to compile your own version that ignores the local copy.

Another is to copy your initial startup file into place on each machine.

Maybe the users could start a small setup script instead of blender (or appears to be blender) that checks existence of user config and copies your initial setup to the users machine from the network drive, obviously not located in the proper startup location and then starts blender.